题目内容
如图所示,粗糙轨道ABC位于竖直平面内,其AB段是半径为R的
圆弧,A点与圆心O等高,BC段水平。轨道处在竖直向下的匀强电场中,电场强度为E。质量为m,带电量为+q的小球从A点由静止下滑,经过B点后又滑行L后停下。已知小球与水平轨道BC之间的动摩擦因数为μ,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538011035476.png)
(1)小球滑到B点时的速度大小;
(2)小球刚要经过B点时对轨道的压力大小;
(3)小球在AB段克服阻力做的功。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153801040262.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538011035476.png)
(1)小球滑到B点时的速度大小;
(2)小球刚要经过B点时对轨道的压力大小;
(3)小球在AB段克服阻力做的功。
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538015551232.png)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538016331010.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538014771028.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538015551232.png)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538016331010.png)
试题分析:解:(1)设小球滑到B点时速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153801695265.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538017731183.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538018361102.png)
(2)设小球在B点受到轨道支持力为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824153801945338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538026001151.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538029591408.png)
根据牛顿第三定律知,小球对轨道的压力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538030681426.png)
(3)设小球在AB段克服阻力做功为W,
由动能定理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538031621183.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241538038331230.png)
点评:本题关键是由水平面上的运动由动能定理求出B点的速度,全过程用动能定理求AB段克服阻力做的功。
![](http://thumb2018.1010pic.com/images/loading.gif)
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